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Finding the Third Proportional to 2,086 and 2,269

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Solution

The third proportional to 2,086 and 2,269 is: 2,468.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,086 : 2,269 = 2,269 : x
  2. Step 2: Convert to fraction form
    2,086/2,269 = 2,269/x
  3. Step 3: Cross multiply
    2,086x = 2,269 × 2,269
  4. Step 4: Simplify right side
    2,086x = 5,148,361
  5. Step 5: Solve for x
    x = 5,148,361/2,086
  6. Step 6: Final answer
    x = 2,468.05

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.